A. Tadeu¹, P. Stanak², J. Antonio¹, J. Sladek², V. Sladek²

CMES-Computer Modeling in Engineering & Sciences, Vol.107, No.5, pp. 345-378, 2015, DOI:10.3970/cmes.2015.107.345

Abstract This paper implements a numerical method based on the mutual coupling of the boundary element method (BEM) and the meshless local Petrov-Galerkin (MLPG) method to simulate elastic wave propagation in fluid-filled boreholes. The fluid-solid interaction is solved in the frequency domain assuming longitudinally invariant geometry in the axial direction (2.5D formulation).
This model is used to assess the influence of the non-homogeneous material properties of a borehole wall that can be caused by a damaged zone, construction process or the ageing of material. The BEM is used to model propagation within the unbounded homogeneous domain and the fluid domain… More >

J. E. Sebold¹, L. A. Lacerda², J. A. M. Carrer³

CMES-Computer Modeling in Engineering & Sciences, Vol.106, No.2, pp. 127-145, 2015, DOI:10.3970/cmes.2015.106.127

Abstract This paper deals with a Finite Element Method (FEM) for the approximation of the Helmholtz equation for two dimensional problems. The acoustic boundary conditions are weakly posed and an auxiliary problem with homogeneous boundary conditions is defined. This auxiliary approach allows for the formulation of a general solution method. Second order finite elements are used along with a discretization parameter based on the fixed wave vector and the imposed error tolerance. An explicit formula is defined for the mesh size control parameter based on Padé approximant. A parametric analysis is conducted to validate the rectangular finite element approach and the… More >

H. Y. Fang^1,2,3, J. Liu⁴, F. M. Wang^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.99, No.6, pp. 473-490, 2014, DOI:10.32604/cmes.2014.099.473

Abstract Construction of electromagnetic wave propagation model in layered pavement structure is a key step in back analysis of ground penetrating radar (GPR) echo signal. The precise integration method (PIM) is a highly accurate, efficient, and unconditionally stable algorithm for solving 1-order ordinary differential equations. It is quite suitable for dealing with problems of wave propagation in layered media. In this paper, forward simulation of GPR electromagnetic wave propagating in homogeneous layered pavement structure is developed by employing PIM. To verify the performance of the proposed algorithm, simulated GPR signal is compared with the measured one. Excellent agreement is achieved. More >

J. E. Sebold¹, L. A. Lacerda², J. A. M. Carrer³

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.2, pp. 111-137, 2014, DOI:10.3970/cmes.2014.103.111

Abstract This work is concerned with the development of the so-called Whitney and Nédélec edge finite element method for the solution of the time-harmonic Maxwell equations. Initially, the second order time harmonic Maxwell systems, as well as their variational formulation, are presented. In the sequence, Whitney and Nédélec element spaces, whose functions present continuous tangential components along the interface are built of adjacent elements. Then, numerical experiments validate the performance of Whitney and Nédélec first order elements in a two-dimensional domain. The discrete dispersion relation for the elements shows that the numerical phase velocity can be used as an error estimator.… More >

Xiaoming Zhang¹, Xingxin Xu^1,2, Yuqing Wang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.1, pp. 1-17, 2014, DOI:10.3970/cmes.2014.100.001

Abstract Orthogonal polynomial approach has been used to deal with the wave propagation in structures that have finite dimension in only one direction, such as horizontally infinite flat plates, axially infinite hollow cylinders. In order to solve wave propagation in two-dimensional piezoelectric rod with rectangular cross section, i.e. the piezoelectric plate with finite dimensions in two directions, an extended orthogonal polynomial approach is proposed in this paper. For validation and illustration purposes, the proposed approach is applied to solving the wave propagation in a square steel rod. The results obtained are in good agreement with the results from the semi-analytical finite… More >

Julieta António¹, António Tadeu^1,2, Patrícia Ferreira³

CMES-Computer Modeling in Engineering & Sciences, Vol.91, No.5, pp. 337-354, 2013, DOI:10.3970/cmes.2013.091.337

Abstract The first of these two companion papers addressed the iterative coupling between a formulation based on the normal derivative of the integral equation (TBEM) and the method of fundamental solutions (MFS), which was used to solve scattering problems involving the propagation of acoustic waves in the vicinity of multiple thin barriers and domes. This second part extends these results to the more complicated case of in-plane wave propagation and presents their application to scattering problems involving SV-P waves. The formulation is first presented and verified by computing the number of iterations required and measuring the CPU time. Afterwards the formulation… More >

Y.J. Ning^1,2,3, Z.Y. Zhao³, J.P. Sun³, W.F. Yuan^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.3, pp. 221-262, 2012, DOI:10.3970/cmes.2012.089.221

Abstract In this paper, wave propagations in jointed rock masses are modeled by the discontinuous deformation analysis (DDA) method. The selection of the numerical control parameters in the DDA for wave propagation modeling is discussed in detail, and the effects of the joint stiffness, the seismic loading frequency, the joint strength, and the incident angle on the propagations of stress waves in a jointed rock mass are modeled and analyzed. Two nonreflecting boundary conditions including the viscous boundary condition (VBC) and the superposition boundary condition (SBC) are coupled into the DDA. The applicability of the two nonreflecting boundary conditions for simple… More >

V. Mallardo¹, M.H. Aliabadi²

CMES-Computer Modeling in Engineering & Sciences, Vol.87, No.2, pp. 77-96, 2012, DOI:10.3970/cmes.2012.087.077

Abstract The present paper intends to couple the Fast Multipole Method (FMM) with the Boundary Element Method (BEM) in the 2D scalar wave propagation. The procedure is aimed at speeding the computation of the integrals involved in the governing Boundary Integral Equations (BIEs) on the basis of the distance between source point and integration element. There are three main contributions. First, the approach is of adaptive type in order to reduce the number of floating-point operations. Second, most integrals are evaluated analytically: the diagonal and off-diagonal terms of the H and G matrices by consolidated techniques, whereas the moment Mk by… More >

B.Y. Tian¹, B. Tie¹, D. Aubry¹, X.Y. Su²

CMES-Computer Modeling in Engineering & Sciences, Vol.76, No.3&4, pp. 217-234, 2011, DOI:10.3970/cmes.2011.076.217

Abstract The present work is devoted to a theoretical analysis and numerical modeling of elastic wave propagation firstly in a one-dimensional periodic elastic rod structure and then in two-dimensional periodic elastic beam structures by using Bloch wave theorem. The dispersion relation between Bloch wave vectors and eigen frequencies is obtained and its dependency upon the micro-structural characteristics of the periodic cellular structure is analyzed. Thanks to the Bloch wave transforms, only the primitive cell is considered theoretically or numerically and the phenomena of frequency band-gaps and the diffracted waves caused by the periodic cells are modeled and analyzed. More >

R. Martin¹, D. Komatitsch^1,2, S. D. Gedney³

CMES-Computer Modeling in Engineering & Sciences, Vol.37, No.3, pp. 274-304, 2008, DOI:10.3970/cmes.2008.037.274

Abstract In the context of the numerical simulation of seismic wave propagation, the perfectly matched layer (PML) absorbing boundary condition has proven to be efficient to absorb surface waves as well as body waves with non grazing incidence. But unfortunately the classical discrete PML generates spurious modes traveling and growing along the absorbing layers in the case of waves impinging the boundary at grazing incidence. This is significant in the case of thin mesh slices, or in the case of sources located close to the absorbing boundaries or receivers located at large offset. In previous work we derived an unsplit convolutional… More >